Formula Reference
Battery Pack Calculator V2.1

// Overhead is placed as a slab at the END of the pack volume // along the LONGEST pack dimension. The slab spans the full // cross-section of the two shorter dimensions. longestAxis = max(PACK_L, PACK_W, PACK_H) // e.g. PACK_L = 363 mm overheadMm = longestAxis × overheadFrac // slab thickness in mm // Available volume for cells (longest dim is reduced by overheadMm): availL = PACK_L - overheadMm (if longestAxis = PACK_L, else PACK_L) availW = PACK_W - overheadMm (if longestAxis = PACK_W, else PACK_W) availH = PACK_H - overheadMm (if longestAxis = PACK_H, else PACK_H) // Available volume (mm³): availVol_mm3 = availL × availW × availH // Equivalently: availVol_mm3 = PACK_VOL × (1 − overheadFrac) // Example (prismatic defaults: PACK_L=363, overhead=15%): overheadMm = 363 × 0.15 ≈ 54.5 mm availL = 363 − 54.5 = 308.5 mm availW = 209 mm (unchanged — not the longest axis) availH = 149 mm (unchanged — not the longest axis) availVol ≈ 308.5 × 209 × 149 ≈ 9,590,000 mm³ (≈ 85% of PACK_VOL)

// All 6 permutations of [cell_L, cell_W, cell_H] are tried // against available pack dims [availL, availW, availH]. // The permutation that maximises totalFit is selected. permutations = [ [L,W,H], [L,H,W], [W,L,H], [W,H,L], [H,L,W], [H,W,L] ] // For each permutation [cL, cW, cH] mapped to [availL, availW, availH]: nL = ⌊(availL + gap) / (cL + gap)⌋ nW = ⌊(availW + gap) / (cW + gap)⌋ nH = ⌊(availH + gap) / (cH + gap)⌋ totalFit = nL × nW × nH // Best permutation = argmax(totalFit) // gap = 2 mm default (thermal clearance + manufacturing tolerance)

// Try all 3 axis orientations (cylinder axis ∥ L, ∥ W, or ∥ H). // Pick the orientation with the highest total cell count. For each orientation (axis aligned to dim X, cross-section Y × Z): nAlong = ⌊(X + endGap) / (cellH + endGap)⌋ inCross = hexPackInArea(Y, Z, d) total = nAlong × inCross // hexPackInArea algorithm (hex close-packing): rowSpacing = d × √3 / 2 // vertical spacing between row centers nEvenCols = ⌊(Y + ε) / d⌋ // cells per even row nOddCols = ⌊(Y − d/2 + ε) / d⌋ // cells per odd row (offset by d/2) Count rows until yPos > Z − d/2: add nEvenCols or nOddCols (alternating) yPos += rowSpacing Best orientation = orientation with max(total) // (all dimensions Y, Z, X are from availL/availW/availH)

// Target pack voltage window: 51–58 V (user-adjustable) minS = ⌈minV / cellV⌉ // min series cells to reach lower voltage bound maxS = ⌊maxV / cellV⌋ // max series cells before exceeding upper voltage bound // For each candidate S in [minS .. maxS]: // P = ⌊totalFit / S⌋ // score = P × S (used cells) // Select S that maximises score (= used cells) usedCells = S × P packV = S × cellV packAh = P × cellAh

packV = S × cellV packAh = P × cellAh packWh = packV × packAh = S × P × cellV × cellAh packKwh = packWh / 1000

PACK_VOL_L = PACK_VOL / 1,000,000 // mm³ → L // Incl. overhead = against total pack envelope (OEM-comparable): WhPerL_incl = packWh / PACK_VOL_L VolUtil_incl = (usedCells × cellVol) / PACK_VOL × 100 // Excl. overhead = against usable cell space only: WhPerL_excl = packWh / (PACK_VOL_L × (1 − overheadFrac)) VolUtil_excl = (usedCells × cellVol) / availVol_mm3 × 100 // Gravimetric density: WhKg = packWh / packWeightKg

// Active Volume Fraction (AVF) = volume of active electrode material // (cathodes + anodes + separators of all cells in the pack) // divided by the volume occupied by the full cell stack // (= usable pack volume after overhead is excluded). // Per-cell active volume: activeVol_per_cell = activeL × activeW × activeH (prismatic — subtracts Al casing walls) activeVol_per_cell = π × (activeD/2)² × activeH (cylindrical — subtracts can wall + caps) // AVF excl. overhead (primary metric; denominator = cell-stack zone only): AVF_excl (%) = (usedCells × activeVol_per_cell) / availVol_mm3 × 100 = (usedCells × activeVol_per_cell) / (PACK_VOL × (1 − overheadFrac)) × 100 // AVF incl. overhead (conservative pack-level figure): AVF_incl (%) = (usedCells × activeVol_per_cell) / PACK_VOL × 100

// Material densities: ρ_cathode = 2.50 g/cm³ (NMC) | 2.30 g/cm³ (LFP) ρ_anode = 1.60 g/cm³ — graphite composite ρ_separator = 1.00 g/cm³ — PE/PP separator membrane ρ_electrolyte = 1.20 g/cm³ — liquid electrolyte ρ_Cu = 8.96 g/cm³ — copper (anode-side CC foil, 8 µm) ρ_Al_CC = 2.70 g/cm³ — aluminum (cathode-side CC foil, 15 µm) ρ_Al_casing = 2.70 g/cm³ — aluminum cell can // Per unit-cell per cm² of electrode face area: w_cathode = ρ_cathode × (cathodeT_µm / 10000) g/cm² w_anode = ρ_anode × (anodeT_µm / 10000) g/cm² w_separator = ρ_separator × (sepT_µm / 10000) g/cm² w_Cu_CC = (CU_DENSITY_KG_M3/1000) × (CU_FOIL_UM / 10000) // ≈ 0.0072 g/cm² w_Al_CC = (AL_CC_DENSITY_KG_M3/1000) × (AL_FOIL_UM / 10000) // ≈ 0.0041 g/cm² w_electrolyte = ρ_electrolyte × ( 0.30 × (cathodeT_µm / 10000) + // 30% cathode porosity 0.35 × (anodeT_µm / 10000) + // 35% anode porosity 0.40 × (sepT_µm / 10000) // 40% separator porosity ) unitCellWtPerCm2 = w_cathode + w_anode + w_separator + w_Cu_CC + w_Al_CC + w_electrolyte // Electrode stack mass: electrodeAreaCm2 = (activeL × activeH) / 100 // mm² → cm² nUnitCells = ⌊activeW / UNIT_CELL_MM⌋ electrodeStackWtG = nUnitCells × unitCellWtPerCm2 × electrodeAreaCm2 // Casing mass (Al shell): casingWtG = (cellVol_mm3 − activeVol_mm3) / 1000 × AL_DENSITY_G_CM3 // Tab / terminal hardware: tabWtG = clamp(cell_L × cell_H / 5000, 3, 15) // 3–15 g, scaled by cell face area // Per-cell mass: cellWeightG = electrodeStackWtG + casingWtG + tabWtG

// Cell stack mass: cellsMassKg = usedCells × cellWeightG / 1000 // Pack-level overhead mass (BMS, bus bars, thermal system, structural housing): // Overhead components fill the overhead slab volume at an average density of 2.0 g/cm³ OVERHEAD_COMPONENT_DENSITY = 2.0 // g/cm³ avg for BMS/busbars/thermal/housing mix overheadVolCm3 = (PACK_VOL × overheadFrac) / 1000 // mm³ → cm³ packOverheadMassKg = overheadVolCm3 × OVERHEAD_COMPONENT_DENSITY / 1000 // Total pack weight: packWeightKg = cellsMassKg + packOverheadMassKg

// CC area: both sides of each unit cell, across all used cells // Each unit cell has 1 Cu CC (anode side) + 1 Al CC (cathode side) // Total CC area = electrode face area × 2 (both sides) × nUnitCells × usedCells ccAreaM2 = (electrodeAreaCm2 / 10000) × 2 × nUnitCells × usedCells // Split evenly between Cu (anode side) and Al (cathode side): cuCost = (ccAreaM2 / 2) × CU_COST_PER_M2 // ≈ $5.40/m² alCost = (ccAreaM2 / 2) × AL_COST_PER_M2 // ≈ $2.40/m² totalCcCost = cuCost + alCost // Cost derivation: CU_COST_PER_M2 = 8×10⁻⁶ m × 8960 kg/m³ × $75.34/kg ≈ $5.40/m² AL_COST_PER_M2 = 15×10⁻⁶ m × 2700 kg/m³ × $59.26/kg ≈ $2.40/m²

// Active bore volume: jrVolMm3 = π × (activeD/2)² × activeH // Unrolled electrode area from bore volume and layer pitch: CYL_LAYER_MM = 0.185 // mm — same bilayer pitch as prismatic ccAreaM2 = (jrVolMm3 / CYL_LAYER_MM / 1e6) × 2 × usedCells // Dual-metal cost: cuCost = (ccAreaM2 / 2) × CU_COST_PER_M2 // Cu anode side ≈ $5.40/m² alCost = (ccAreaM2 / 2) × AL_COST_PER_M2 // Al cathode side ≈ $2.40/m² totalCcCost = cuCost + alCost

// One mono-cell = one bipolar layer: // cathode coating + separator + anode coating + PCC CC layer monoCellT_µm = cathodeT + sepT + anodeT + beyondT monoCellT_mm = monoCellT_µm / 1000 // Default thicknesses (user-adjustable): // cathodeT = 50 µm, sepT = 10 µm, anodeT = 90 µm, beyondT = 10 µm // → monoCellT_mm = 160 µm = 0.160 mm // Sub-stack (nSeries bipolar layers stacked in series): nSeries = round((minV + maxV) / 2 / cellV), clamped to [minS, maxS] subStackT = nSeries × monoCellT_mm // total thickness subStackX = activeX + 2 × sealW // sealed length subStackY = activeY + 2 × sealW // sealed width (sealW = 1 mm sealing margin) // Packing — same overhead mechanism as prismatic/cylindrical: // Overhead slab placed along longest pack axis (getOverheadDims) // PCC avail dims = availL, availW, availH nParallel = ⌊availL / subStackX⌋ × ⌊availW / subStackY⌋ × ⌊availH / subStackT⌋ × (1 − OVERHEAD_BEYOND) // fractional reduction via geometric count × (1-overhead) → ⌊nParallel_geo × (1 − OVERHEAD_BEYOND)⌋

// Areal capacity → per-mono-cell capacity: activeAreaCm2 = (activeX × activeY) / 100 // mm² → cm² monoAh = (arealCap_mAhcm2 × activeAreaCm2) / 1000 // Pack totals: packAh = nParallel × monoAh packV = nSeries × cellV packWh = packV × packAh // Weight model (layer-by-layer, no Cu or Al foil): ρ_cathode = 2.50 g/cm³ (NMC) | 2.30 g/cm³ (LFP) ρ_anode = 1.60 g/cm³ ρ_sep = 1.00 g/cm³ ρ_beyond = 1.05 g/cm³ // Per mono-cell per cm² active area: monoWeightPerCm2 = ρ_cathode×(cathodeT/10000) + ρ_anode×(anodeT/10000) + ρ_sep×(sepT/10000) + ρ_beyond×(beyondT/10000) subStackWeightG = nSeries × monoWeightPerCm2 × activeAreaCm2 packWeightKg = (nParallel × subStackWeightG) / 1000

// Total CC area across all sub-stacks: ccAreaPerSubStack_m2 = nSeries × (activeAreaCm2 / 10000) totalCcArea_m2 = nParallel × ccAreaPerSubStack_m2 // Traditional baseline — full-area Cu (anode) + full-area Al (cathode) per interface: ccCuCost = totalCcArea_m2 × CU_COST_PER_M2 // ≈$5.40/m² ccAlCost = totalCcArea_m2 × AL_COST_PER_M2 // ≈$2.40/m² ccCostTraditional = ccCuCost + ccAlCost // ≈$7.80/m² // PCC replacement cost: pccCostTotal = totalCcArea_m2 × BEYOND_COST_PER_M2 // $0.89/m² // Savings: savings = ccCostTraditional − pccCostTotal savingsPct = savings / ccCostTraditional × 100 // ≈ 88.6%

// Objective: find (L, W, H) that maximises pack energy (Wh) // subject to the current overhead % and voltage constraints. pOh = getOverheadDims(OVERHEAD_PRISMATIC) aL = pOh.availL, aW = pOh.availW, aH = pOh.availH for L in [30 .. aL] step 8: for W in [10 .. aW] step 5: for H in [20 .. aH] step 5: // Cell count: nL = ⌊(aL + gap) / (L + gap)⌋ nW = ⌊(aW + gap) / (W + gap)⌋ nH = ⌊(aH + gap) / (H + gap)⌋ totalFit = nL × nW × nH if totalFit < minS: skip // can't even reach min voltage // Best S×P: { s, p } = getBestSeries(totalFit, cellV, minV, maxV) if p == 0: skip // Estimate energy using cell-level energy density: cellVol_L = L × W × H / 1e6 cellAh = eDens_WhL × cellVol_L / cellV // eDens ≈ 290 Wh/L NMC, 200 Wh/L LFP energyWh = s × p × cellV × cellAh if energyWh > bestWh: record as best // Output: best (L, W, H) — shown as suggested dims in the UI

// Only evaluates the 4 established commercial formats: formats = [ { name: "18650", d: 18, cellH: 65 }, { name: "21700", d: 21, cellH: 70 }, { name: "46800", d: 46, cellH: 80 }, { name: "46900", d: 46, cellH: 90 } ] // For each format × 3 axis orientations: // 1. Hex pack into available dims → usedCells // 2. getBestSeries → S, P // 3. Derive cellAh from jelly-roll geometry + areal capacity // 4. energyWh = S × P × cellV × cellAh // Return format with highest energyWh

// Sweep electrode face dimensions (X, Y) to maximise pack energy. pOh = getOverheadDims(OVERHEAD_BEYOND) aL = pOh.availL, aW = pOh.availW, aH = pOh.availH for X in [50 .. aL] step 10: for Y in [50 .. aH] step 10: // note: Y sweeps across aH (height axis) subStackX = X + 2 × sealW // add sealing margin subStackY = Y + 2 × sealW nSeries = round((minV + maxV) / 2 / cellV), clamped to [minS, maxS] subStackT = nSeries × monoCellT_mm nParallel = ⌊aL/subStackX⌋ × ⌊aW/subStackY⌋ × ⌊aH/subStackT⌋ monoAh = arealCap × (X × Y / 100) / 1000 // cm² conversion energyWh = nSeries × cellV × nParallel × monoAh if energyWh > bestWh: record as best (X, Y) // Output: best (activeX, activeY) — displayed in the UI recommendation chip